Revealing mistake: When McClane is hanging on the steel cable which pulls their car to the river, right when he says "Run, run" there's a brief shot and it's very obvious that the guy is Bruce Willis's stunt double.
Revealing mistake: When the bomb explodes at Bonwit Tellers at the start, we see a van fly into the air. You can see the devices that throw it upwards.
Chosen answer: He sees the reflection of his friend's badge number that he remembered from their conversation about the lottery earlier, so knows the badge was taken from his dead friend.
Captain Defenestrator